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A fast regularized least-squares method for retinal vascular oxygen tension estimation using a phosphorescence lifetime imaging model.

Gunay G, Yildirim I - Biomed Eng Online (2013)

Bottom Line: In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates.This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

View Article: PubMed Central - HTML - PubMed

Affiliation: Electrical and Electronics Engineering Department, Istanbul Technical University, 34469 Istanbul, Turkey. iyildirim@itu.edu.tr.

ABSTRACT

Background: Monitoring retinal oxygenation is of primary importance in detecting the presence of some common eye diseases. To improve the estimation of oxygen tension in retinal vessels, regularized least-squares (RLS) method was shown to be very effective compared with the conventional least-squares (LS) estimation. In this study, we propose an accelerated RLS estimation method for the problem of assessing the oxygenation of retinal vessels from phosphorescence lifetime images.

Methods: In the previous work, gradient descent algorithms were used to find the minimum of the RLS cost function. This approach is computationally expensive, especially when the oxygen tension map is large. In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates. This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.

Results: Performance analyses are conducted using both real and simulated data sets. In terms of computational complexity, the proposed RLS estimation method is significantly better than RLS methods that use gradient descent algorithms to find the minimum of the cost function. Additionally, there is no significant difference between the estimates acquired by the proposed and conventional RLS estimation methods.

Conclusion: The proposed RLS estimation method for computing the retinal oxygen tension is computationally efficient, and produces estimates with negligible difference from those obtained by iterative RLS methods. Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

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Oxygen tension map (600 × 425 pixels) of a rat generated using the LS (1), iterative RLS (2), and the proposed RLS (3) methods. The color bar shows oxygen tension in millimeters of mercury.
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Figure 3: Oxygen tension map (600 × 425 pixels) of a rat generated using the LS (1), iterative RLS (2), and the proposed RLS (3) methods. The color bar shows oxygen tension in millimeters of mercury.

Mentions: We use both simulated and real oxygen tension maps (Figures 2 and 3, respectively) in our experiments. The real retinal oxygen tension map used in this study was acquired from a Long Evans pigmented rat (~500 g) using a novel system described in [6]. The animal was treated according to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. In order to anesthetize the rat, an intra-peritoneal infusion of Ketamine (85 mg/kg IP) and Xylazine (3.5 mg/kg IP) at the respective rates of 0.5 mg/kg/min and 0.02 mg/kg/min was used. Before and during the imaging, gas mixture containing 21% oxygen (room air, normoxia) was administered to rats for 5 minutes. Pd-porphine (Frontier Scientific, Logan, Utah), an oxygen-sensitive molecular probe, was dissolved (12 mg/ml) in bovine serum albumin solution (60 mg/ml) and physiological saline buffered to a pH of 7, and injected intravenously (20 mg/kg). Imaging was conducted at areas within two-disk diameters (600 microns) from the edge of the optic nerve head. For each pixel location, 10 phase-delayed optical section phosphorescence lifetime intensity images were acquired with a corresponding phase delay increments of 74 μs, and then these intensity images were brought together to form en-face phosphorescence images of the retinal vasculatures in the retinal plane. To generate the simulated data we used in this work, physiological features and topology of real retinal vessels were followed based on the previous studies [6-8,15]. Near the optic disc, which has a diameter nearly 300 microns [21], venous and arterial oxygen tensions of rat retina vary around 35 mm-Hg and 60 mm-Hg, respectively in the normoxia condition. As getting far from the optic disc, arterial oxygen tension decreases almost linearly while venous oxygen tension remains almost the same [15]. Since the iterative method requires a considerable amount of time as size of the pO2 map gets larger, the simulated pO2 map was generated to be 485x600 pixels. But it should be noted that this size is not a limitation to the proposed method. In the simulations, we add i.i.d. white Gaussian noise with 15, 20, and 25 dB SNR to the phosphorescence lifetime images.


A fast regularized least-squares method for retinal vascular oxygen tension estimation using a phosphorescence lifetime imaging model.

Gunay G, Yildirim I - Biomed Eng Online (2013)

Oxygen tension map (600 × 425 pixels) of a rat generated using the LS (1), iterative RLS (2), and the proposed RLS (3) methods. The color bar shows oxygen tension in millimeters of mercury.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3818002&req=5

Figure 3: Oxygen tension map (600 × 425 pixels) of a rat generated using the LS (1), iterative RLS (2), and the proposed RLS (3) methods. The color bar shows oxygen tension in millimeters of mercury.
Mentions: We use both simulated and real oxygen tension maps (Figures 2 and 3, respectively) in our experiments. The real retinal oxygen tension map used in this study was acquired from a Long Evans pigmented rat (~500 g) using a novel system described in [6]. The animal was treated according to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. In order to anesthetize the rat, an intra-peritoneal infusion of Ketamine (85 mg/kg IP) and Xylazine (3.5 mg/kg IP) at the respective rates of 0.5 mg/kg/min and 0.02 mg/kg/min was used. Before and during the imaging, gas mixture containing 21% oxygen (room air, normoxia) was administered to rats for 5 minutes. Pd-porphine (Frontier Scientific, Logan, Utah), an oxygen-sensitive molecular probe, was dissolved (12 mg/ml) in bovine serum albumin solution (60 mg/ml) and physiological saline buffered to a pH of 7, and injected intravenously (20 mg/kg). Imaging was conducted at areas within two-disk diameters (600 microns) from the edge of the optic nerve head. For each pixel location, 10 phase-delayed optical section phosphorescence lifetime intensity images were acquired with a corresponding phase delay increments of 74 μs, and then these intensity images were brought together to form en-face phosphorescence images of the retinal vasculatures in the retinal plane. To generate the simulated data we used in this work, physiological features and topology of real retinal vessels were followed based on the previous studies [6-8,15]. Near the optic disc, which has a diameter nearly 300 microns [21], venous and arterial oxygen tensions of rat retina vary around 35 mm-Hg and 60 mm-Hg, respectively in the normoxia condition. As getting far from the optic disc, arterial oxygen tension decreases almost linearly while venous oxygen tension remains almost the same [15]. Since the iterative method requires a considerable amount of time as size of the pO2 map gets larger, the simulated pO2 map was generated to be 485x600 pixels. But it should be noted that this size is not a limitation to the proposed method. In the simulations, we add i.i.d. white Gaussian noise with 15, 20, and 25 dB SNR to the phosphorescence lifetime images.

Bottom Line: In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates.This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

View Article: PubMed Central - HTML - PubMed

Affiliation: Electrical and Electronics Engineering Department, Istanbul Technical University, 34469 Istanbul, Turkey. iyildirim@itu.edu.tr.

ABSTRACT

Background: Monitoring retinal oxygenation is of primary importance in detecting the presence of some common eye diseases. To improve the estimation of oxygen tension in retinal vessels, regularized least-squares (RLS) method was shown to be very effective compared with the conventional least-squares (LS) estimation. In this study, we propose an accelerated RLS estimation method for the problem of assessing the oxygenation of retinal vessels from phosphorescence lifetime images.

Methods: In the previous work, gradient descent algorithms were used to find the minimum of the RLS cost function. This approach is computationally expensive, especially when the oxygen tension map is large. In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates. This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.

Results: Performance analyses are conducted using both real and simulated data sets. In terms of computational complexity, the proposed RLS estimation method is significantly better than RLS methods that use gradient descent algorithms to find the minimum of the cost function. Additionally, there is no significant difference between the estimates acquired by the proposed and conventional RLS estimation methods.

Conclusion: The proposed RLS estimation method for computing the retinal oxygen tension is computationally efficient, and produces estimates with negligible difference from those obtained by iterative RLS methods. Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

Show MeSH
Related in: MedlinePlus